Link Prediction Based On Higher Order Structures In Complex Networks

With the rapid development of information technology represented by the Internet and5 G,the production and life of human society are increasingly dependent on various complex systems.For example,The social network formed by social platforms such as We Chat and Facebook and the scientific research cooperation network,and so on.Complex networks are topology structure composed of nodes and their edges.It is an important research topic in network science to explore the dynamic evolution mechanism on various networks,and then make predictions and control.During the evolution of the network,the interaction between nodes is a binary interaction,but in many cases it is the interaction behavior of a group.It is of great significance to study the impact of higher-order interactions on the network structure.How to use high-order topological information to analyze the network and predict its evolution trend is an important research topic in network science.This paper focuses on how to combine high-order structural information to build a graph neural network model,and then explore the evolution mechanism of networks and predict network structure.The work of the article is mainly divided into the following aspects:· How to effectively combine high-order structure information and graph neural networks for network link prediction?· How to fuse high-order information into dynamic networks and learn the evolution pattern of networks more efficiently?· Combined with the network topology and dynamic process,how to effectively control the stateof network target links and the evolution of the corresponding topology?1.It is found that the motif structure can improve the expressive ability of graph convolution network,a graph convolution network model based on motif is proposed,and the effectiveness of link prediction task is verified by combining with the autoencoder framework.Under the auto-encoder framework,a motif-based graph convolution network model is proposed,which gives a low-dimensional vector representation of the network.In the encoding part,on the basis of constructing the motif adjacency matrix,aggregate neighbor information for each type of motif to represent the nodes and fuse the corresponding representations of various motifs.Finally,the self-attention model based on the motif to give The node vector representation is shown.The decoding part adopts the method of vector inner product to obtain the node similarity score.The innovation of the model is to give a graph neural network link prediction model that fuses motif information and auto-encoders.The results on different data sets show that the fusion of network motif information fully improves the expressive ability of the model,and it is better than most baseline methods in network link prediction tasks.The motif structure and the graph attention network model were further integrated to construct a motif attention network model MGAT(Motif-based Graph Attention Neural Network).The innovation point is to make full use of the high-order topological information of the network to construct a graph attention network model based on motif information.At the same time,in the process of predicting the network structure,the distance between nodes is integrated into the decoder,which improves the link prediction of the model.performance.Experimental results on several types of citation networks and social networks show that the model significantly improves the expressive ability of graph neural networks and shows good performance in link prediction.2.The importance of high-order topology in dynamic networks is discovered,and a representation learning method that integrates high-order topology and time-series convolution networks is proposed to further improve dynamic network representation capabilities.In order to explore the dynamic evolution mode and law of the network,a motif-based temporal Convolution network link prediction model MTCN(Motif-based Temporal Convolution Network)is proposed.For the network at each moment in the specified time window,the model uses the attention model based on the motif structure to obtain the representation of the network at each moment under the specified motif.On this basis,the network representations under various motifs are used as network structural features,and temporal features are learned with the help of a one-dimensional causal convolution model.Further,a motif attention model based on a temporal network is constructed,which combines the representations of various motifs to obtain the final node representation.Finally,we combines the auto-regressive model to predict the network at the next moment structure.The innovation point is to integrate the motif information into the time series model,and learn the dynamic evolution trend of the motif.Link prediction experiments are carried out on the communication network and the scoring network respectively,and the effectiveness of the model is verified.3.For the control problem of edge state in network,a k-travel model based on target control on edge dynamics is proposed,and an optimization scheme for controlling the target edges is provided.The purpose of exploring the evolution mechanism of the network is to control the network reasonably so that the network evolves in a direction that is beneficial to human beings.In order to study how to effectively control the network state based on the edge dynamics model of the complex network,a k-travel model based on the edge dynamics target control is established for the tree network.For the general network structure,on the basis of constructing the recursive double-layer bipartite network,a greedy algorithm TEC(Target Edge Control)for calculating the least control input is given.The innovation of this chapter is to give a new scheme to calculate the control.In the experiments of two types of artificial networks and multiple real networks,the topological factors affecting the control efficiency are analyzed and the TEC algorithm is verified to be superior to the traditional structural control method on control efficiency in most networks.